(3x+y)(3x+y)=0

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Solution for (3x+y)(3x+y)=0 equation: 


Simplifying
(3x + y)(3x + y) = 0

Multiply (3x + y) * (3x + y)
(3x * (3x + y) + y(3x + y)) = 0
((3x * 3x + y * 3x) + y(3x + y)) = 0

Reorder the terms:
((3xy + 9x2) + y(3x + y)) = 0
((3xy + 9x2) + y(3x + y)) = 0
(3xy + 9x2 + (3x * y + y * y)) = 0
(3xy + 9x2 + (3xy + y2)) = 0

Reorder the terms:
(3xy + 3xy + 9x2 + y2) = 0

Combine like terms: 3xy + 3xy = 6xy
(6xy + 9x2 + y2) = 0

Solving
6xy + 9x2 + y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3x + y)(3x + y) = 0


Subproblem 1
Set the factor '(3x + y)' equal to zero and attempt to solve:

Simplifying
3x + y = 0

Solving
3x + y = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1y' to each side of the equation.
3x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
3x + 0 = 0 + -1y
3x = 0 + -1y
Remove the zero:
3x = -1y

Divide each side by '3'.
x = -0.3333333333y

Simplifying
x = -0.3333333333y

Subproblem 2
Set the factor '(3x + y)' equal to zero and attempt to solve:

Simplifying
3x + y = 0

Solving
3x + y = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1y' to each side of the equation.
3x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
3x + 0 = 0 + -1y
3x = 0 + -1y
Remove the zero:
3x = -1y

Divide each side by '3'.
x = -0.3333333333y

Simplifying
x = -0.3333333333y
Solution
x = {-0.3333333333y, -0.3333333333y}

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